1. Field of the Invention
This invention relates to methods and apparatus for optical sensing, including counting and sizing of individual particles of varying size in a fluid suspension, and more particularly, to such methods and apparatus which yield higher sensitivity and coincidence concentration than can be realized by optical sensors of conventional design.
2. Description of Related Art
It is useful to review the principles underlying the traditional method of optical particle counting, hereinafter referred to as single-particle optical sensing (SPOS). Sensors that are used to implement SPOS are based on the physical technique of light extinction (LE) or light scattering (LS), or some combination of the two. The optical design of a traditional SPOS sensor based on the LE technique is shown schematically in FIG. 1. A fluid, consisting of a gas or liquid, in which particles of various sizes are suspended, is caused to flow through a physical flow channel 10, typically of rectangular cross section. Two of the opposing parallel surfaces 12 and 14 defining the flow channel are opaque, while the remaining two opposing parallel surfaces 16 and 18 perpendicular to the opaque pair are transparent, comprising the xe2x80x9cfrontxe2x80x9d and xe2x80x9cbackxe2x80x9d windows of the flow cell 10. A beam of light 20 of appropriate shape enters front window 16 of flow cell 10, passes through the flowing fluid and particles, exits flow cell 10 through back window 18 and impinges on a relatively distant light-extinction detector DLE.
The width of front and back windows 16 and 18 along the direction defined by the x-axis is defined as xe2x80x9caxe2x80x9d (FIG. 1). The depth of flow cell 10, along the direction defined by the y-axis, parallel to the axis of the incident light beam, is defined as xe2x80x9cb.xe2x80x9d Suspended particles of interest are caused to pass through flow cell 10 along the direction defined by the z-axis (from top to bottom in FIG. 1) at a steady, appropriate rate of flow, F, expressed in units of milliliters (ml) per second, or minute.
The optical sensing zone 22 (xe2x80x9cOSZxe2x80x9d), or xe2x80x9cview volume,xe2x80x9d of the sensor is the thin region of space defined by the four internal surfaces of flow channel 10 and the ribbon-like beam of light that traverses channel 10. The resulting shape of the OSZ resembles a thin, approximately rectangular slab (having concave upper and lower surfaces, as described below), with a minimum thickness defined as 2w, oriented normal to the longitudinal axis of flow cell 10 (FIG. 1). Source of illumination 24 is typically a laser diode, having either an elliptical- or circular-shaped beam, with a gaussian intensity profile along each of two mutually orthogonal axes and a maximum intensity at the center of the beam. Two optical elements are typically required to create the desired shape of the incident light beam that, together with the front and back windows of the flow channel 10, defines the OSZ. The first optical element is usually a lens 26, used to focus the starting collimated beam at the center (x-y plane) of flow cell 10. The focused beam xe2x80x9cwaist,xe2x80x9d or width, 2w, is proportional to the focal length of the lens and inversely proportional to the width of the starting collimated beam, defined by its 1/e2 intensity values. The focused beam width, 2w, also depends on the orientation of the beam, if its cross section is not circular.
The second optical element is typically a cylindrical lens 28, used to xe2x80x9cdefocus,xe2x80x9d and thereby widen, the light beam in one directionxe2x80x94i.e. along the x-axis. In effect, cylindrical lens 28 converts what otherwise would be a uniformly focused beam (of elliptical or circular cross section) impinging on the flow cell, into a focused xe2x80x9cline-sourcexe2x80x9d that intersects flow channel 10 parallel to the x-axis. The focal length and location of cylindrical lens 28 are chosen so that the resulting beam width (defined by its 1/e2 intensity points) along the x-axis at the center of the flow cell is much larger than the width, a, of the flow channel 10. As a result, front window 16 of the sensor captures only the top portion of the gaussian beam, where the intensity is nearly uniform. Substantial uniformity of the incident intensity across the width (x-axis) of the flow channel 10 is essential in order to achieve optimal sensor resolution. The intensity profile along the z-axis of the resulting ribbon-like light beam is also gaussian, being brightest at the center of the OSZ and falling to 1/e2 at its xe2x80x9cupperxe2x80x9d and xe2x80x9clowerxe2x80x9d edges/faces, where the distance between these intensity points defines the thickness, 2w, of the OSZ.
The shape of the OSZ 22 deviates from that of an idealized, rectangular slab shape suggested in FIG. 1. Rather, the cross-sectional shape of the OSZ in the y-z plane resembles a bow tie, or hourglass, owing to the fact that the incident light beam is focused along the y-axis. However, assuming that the optical design of the sensor has been optimized, the focal length of the focusing lens will be much larger than the depth, b, of the flow cell. Therefore, the xe2x80x9cdepth of fieldxe2x80x9d of the focused beamxe2x80x94defined as the distance between the two points along the y-axis at which the beam thickness expands to 2xc3x972wxe2x80x94will be significantly larger than the depth, b, of the flow cell. Consequently, the variation in light intensity will be minimal along the y-axis.
The ribbon-like light beam passes through the fluid-particle suspension and impinges on a suitable light detector DLE (typically a silicon photodiode). In the absence of a particle in the OSZ, detector DLE receives the maximum illumination. A particle that passes through the OSZ momentarily xe2x80x9cblocksxe2x80x9d a small fraction of the incident light impinging on detector DLE, causing a momentary decrease in the photocurrent output of detector DLE and the corresponding voltage xe2x80x9cVLExe2x80x9d produced by suitable signal-conditioning means. The resulting signal consists of a negative-going pulse 30 of height xcex94VLE, superimposed on a d.c. xe2x80x9cbaselinexe2x80x9d level 32 of relatively large magnitude, V0, shown schematically in FIG. 2. Obviously, the larger the particle, the larger the pulse height, xcex94VLE, both in absolute magnitude and as a fraction of V0.
The detector signal, VLE, is processed by an electronic circuit 34, which effectively removes the baseline voltage, V0, typically either by subtracting a fixed d.c. voltage from VLE or by xe2x80x9ca.c. coupling,xe2x80x9d using an appropriate high-pass filter. This action allows for capture of the desired negative-going pulses of various heights, xcex94VLE. The resulting signal pulses are then xe2x80x9cconditionedxe2x80x9d further, typically including inversion and amplification. Each pulse is digitized using a fast, high-resolution analog-to-digital (A/D) converter, allowing its height to be determined with relatively high accuracy. A calibration table is generated, using a series of xe2x80x9cstandardxe2x80x9d particles (typically polystyrene latex spheres) of known diameter, d, spanning the desired size range. This set of discrete values of xcex94VLE vs d is stored in computer memory and typically displayed as log xcex94VLE vs log d, with a continuous curve connecting the points. The set of measured pulse heights, xcex94VLE, are easily converted to a set of particle diameters, d, by interpolation of the calibration table values.
In principle, there are several physical mechanisms that can contribute to the light extinction effect. These include refraction, reflection, diffraction, scattering and absorbance. The mechanisms of refraction and reflection dominate the LE effect for particles significantly larger than the wavelength of the incident light, typically 0.6-0.9 micrometers (xcexcm). In the case of refraction, the light rays incident on a particle are deflected toward or away from the axis of the beam, depending on whether the refractive index of the particle is larger or smaller, respectively, than the refractive index of the surrounding fluid. Provided the two refractive indices differ sufficiently and the (small) detector element, DLE, is located sufficiently far from the flow cell, the refracted rays of light will diverge sufficiently that they fail to impinge on detector DLE, thus yielding the desired signal, xcex94VLE. The mechanism of reflection necessarily accompanies refraction, and the greater the refractive index xe2x80x9ccontrastxe2x80x9d between the particles and fluid, the greater the fraction of incident light reflected by the particle. The phenomenon of diffraction typically has a negligible effect on the LE signal, because the angles associated with the major intensity maxima and minima are smaller than the typical solid angle defined by the distant detector DLE.
By contrast, however, the light scattering phenomenon typically makes an important contribution to the LE signal. It is the dominant mechanism for particles comparable in size to, or smaller than, the wavelength of the incident light. The magnitude and angular distribution of the scattered light intensity depends on the size, shape and orientation of the particle, as well as the contrast in refractive index and the wavelength of the beam. The well-known Mie and Rayleigh scattering theories describe in detail the behavior of the light scattering intensity. The greater the amount of light scattered off-axis, away from the axis of the incident light beam, the smaller the light flux that reaches the extinction detector DLE.
The mechanism of absorbance may be significant for particles that are highly pigmented, or colored. The magnitude of this effect depends on the wavelength of the incident light, as well as the size of the particle. The contribution of absorbance to the overall LE signal may be significant for particles significantly larger than the wavelength.
There is a simple, approximate relationship between the particle size and the magnitude of the LE signal, xcex94VLE. The total light flux incident on the detector, DLE, in the absence of a particle in the OSZ is proportional to the area of illumination, A0. This is approximated by
A0≈2awxe2x80x83xe2x80x83(1)
Assuming that the intensity of the beam incident on the flow channel 10 is uniform along both its width, a, and over the thickness, 2w, of the beam (i.e. assumed to have a rectangular, rather than gaussian, profile).
If one makes the additional simplifying assumption that a particle completely blocks the light that impinges on it (i.e. perfect, 100% extinction), then the fraction of incident light blocked by the particle is given by xcex94A/A0, where xcex94A represents the cross-sectional area of the particle. The pulse height, xcex94VLE, of the light-extinction signal for particle diameters  less than 2w can then be expressed by
xcex94VLE=(xcex94A/A0)V0xe2x80x83xe2x80x83(2)
For simplicity, the particles are assumed to be spherical and homogeneous, in order to avoid complicating details related to particle shape and orientation. Quantity xcex94A for a particle of diameter d is therefore given by
xe2x80x83xcex94A=xcfx80d2/4xe2x80x83xe2x80x83(3)
In cases where the particle blocks less than 100% of the light incident on itxe2x80x94e.g. where the dominant mechanism for extinction is mostly light scattering, rather than refraction and reflectionxe2x80x94quantity xcex94A represents the xe2x80x9ceffectivexe2x80x9d cross-sectional area, smaller than the actual physical area.
The velocity, v, of the particles that pass through the OSZ is given by
v=F/abxe2x80x83xe2x80x83(4)
The pulse width, xcex94t, represents the time of transit of the particle through the OSZxe2x80x94i.e. between the 1/e2 intensity points that define the width, 2w. Neglecting the size of the particle compared to quantity 2w, the pulse width is given by
xcex94t=2w/vxe2x80x83xe2x80x83(5)
It is instructive to calculate the values of the parameters above for a typical LE sensorxe2x80x94the Model LE400-1E sensor (Particle Sizing Systems, Santa Barbara, Calif.), with a=400 xcexcm, b=1000 xcexcm, and 2w≈35 xcexcm, assuming F=60 ml/min.
A0=1.4xc3x97104 xcexcm2
v=250 cm/sec
xcex94t=14xc3x9710xe2x88x926 sec=14 xcexcsec
The smallest particle diameter that typically can be reliably detected (i.e. where xcex94VLE exceeds the typical r.m.s. noise level by at least a 2:1 ratio) is approximately 1.3 xcexcm. This corresponds to a physical blockage ratio, xcex94A/A0, of 0.000095, or less than 0.01%.
Increasing the intensity of the light source should, in theory, have no influence on the sensitivity, or lower particle size limit, of an extinction-type sensor. For a given baseline voltage, V0, the pulse height, xcex94VLE, depends only on the fraction of the illuminated detector area effectively blocked by the particle, xcex94A/A0. (The effect of sample turbidity is discussed later.) Only if a more powerful light source possesses lower noise, will the sensor be able to detect reliably a smaller fractional change in effective blocked area, and therefore a smaller particle diameter. However, any such improvement in performance, due to increased S/N ratio, represents only a second-order effect and is usually not significant.
Using the parameters for the LE-type sensor discussed above, one obtains an estimate of the effective volume, VOSZ, of the OSZ,
VOSZ=2abw=1.4xc3x97107 xcexcm3=1.4xc3x9710xe2x88x925 cm3xe2x80x83xe2x80x83(6)
The reciprocal of the OSZ volume, 1/VOSZ, equals the number of xe2x80x9cview volumesxe2x80x9d contained in 1 cm3 (i.e. 1 ml) of fluidxe2x80x94i.e. 1/VOSZ≈7xc3x97104 for the example above.
The quantity 1/VOSZ provides a measure of the xe2x80x9ccoincidence limitxe2x80x9d of the sensorxe2x80x94the concentration (# particles/ml) at which the particles pass one at a time through the OSZ, provided they are spaced uniformly throughout the fluid, with each particle effectively occupying one view volume at any given time. In reality, of course, the particles are located randomly throughout the fluid. Therefore, the particle concentration must be reduced substantially with respect to this xe2x80x9cidealxe2x80x9d valuexe2x80x94i.e. by 10:1 or morexe2x80x94in order to ensure the presence of only one particle at a time in the OSZ. The actual coincidence limit of the sensor is usually defined as the concentration at which only 1% of the particle counts are associated with two or more particles passing through the OSZ at the same time, possibly giving rise to a single detected pulse of exaggerated pulse height. Hence, the useful coincidence limit of the sensor is typically only 10% (or less) of the value 1/VOSZ. Using the example above, this implies a coincidence concentration of approximately 7,000 particles/ml. In practice the coincidence limit of a sensor of given design will also be a function of particle size. The value indicated is appropriate in the case of very fine particles, having diameters much smaller than the effective thickness, 2w, of the OSZ. The coincidence limit may be significantly lower in the case of particles comparable in size to, or larger than, parameter 2w. Therefore, in practice one often chooses to collect data at a particle concentration of only 50% (or less) of the value given above, in order to eliminate erroneous particle xe2x80x9ccountsxe2x80x9d and distortion of the resulting particle size distribution (PSD).
For applications involving concentrated suspensions and dispersions, it is very desirable to increase the coincidence concentration of the sensor, so that less extensive dilution of the starting sample is required. First, this improvement lowers the volume of clean fluid needed to dilute the sample and reduces the extent to which the diluent fluid must be free of particle contamination. Second, and more important, extensive dilution of the starting concentrated suspension may not be feasible, if it results in significant changes in the PSDxe2x80x94e.g. due to promotion of particle agglomeration. Examples include pH-sensitive oxide xe2x80x9cslurriesxe2x80x9d used for processing semiconductor wafers by the method known as chemical mechanical planarization (CMP). Also, for a variety of applications it is useful, if not essential, to increase the sensitivity of the SPOS methodxe2x80x94i.e. to reduce the minimum detectable particle size. Increases in the coincidence concentration and improvements in the sensitivity of LE-type sensors are usually related, and there are several ways in which improvements in both parameters can be achieved.
The most obvious way in which the sensitivity of an extinction-type sensor can be improved is to decrease the cross-sectional area of illumination, A0. Using the example above, this is accomplished by decreasing the lateral cell dimension, a, or the incident beam thickness, 2w, or both. Concerning the latter course of action, the effective thickness, 2w, of the OSZ can be reduced only to a limited extent. This limitation is imposed by the relationship between the focal length of the focusing lens, the depth of the flow cell, and the width of the starting light beam. Given the nature of gaussian beam optics and the limitations imposed by diffraction, it is impractical to decrease parameter 2w below approximately 5 xcexcm. This reduction represents only a 7-fold improvement over the 35-xcexcm value assumed in the example above. Furthermore, in order to achieve relatively high size resolution for smaller particles, it is useful to retain the quadratic dependence of the light-extinction pulse height, xcex94VLE, on the particle diameter, d, which obtains only for values of d (substantially) smaller than 2w. Hence, in order to achieve optimal performance for many important applications, it is usually not desirable to make the thickness of the OSZ appreciably thinner than about 10 xcexcm.
Instead, it appears to be more attractive to reduce the lateral dimension, a, of the OSZxe2x80x94e.g. from 400 xcexcm (using the example above) to 40 xcexcm. To a first approximation (ignoring nonlinear signal/noise effects), this 10-fold reduction in A0 results in a similar 10-fold reduction in the effective cross-sectional area, xcex94ALE, required to achieve a given fraction of blocked area, xcex94ALE/A0.
There is a second significant advantage that results from this 10-fold reduction of the width of the flow channel 10. The volume of the OSZ (Equation 6) is also reduced 10-fold, resulting in a reduction of the coincidence concentration by the same factor. Hence, the working sample concentration can be increased 10-fold, permitting a 10-fold lower extent of dilution required for the starting concentrated particle dispersion. Of course, the same 10-fold increase in the coincidence concentration can be achieved through a 10-fold reduction in the cell depth, b, rather than the cell width, a, considered above. However, the improvement in sensor sensitivity would no longer be obtained. Clearly, while dimensions xe2x80x9caxe2x80x9d and xe2x80x9cbxe2x80x9d play equivalent roles with respect to determining VOSZ, and therefore the coincidence concentration, they are not equivalent with respect to influencing sensor sensitivity.
Unfortunately, there is a serious disadvantage to this proposed approach. It is not practical to reduce dimension a (or b, for that matter) to such an extent (i.e. significantly smaller than 100 xcexcm) for reasons that are obvious to anyone familiar with the use of SPOS technology. Such a small dimension virtually invites clogging of the flow channel 10, due to the inevitable existence of contaminant (xe2x80x9cdirtxe2x80x9d) particles in the diluent fluid and/or large particles associated with the sample, such as over-size xe2x80x9coutliersxe2x80x9d and agglomerates of smaller xe2x80x9cprimaryxe2x80x9d particles. Generally, the minimum lateral dimension (either a or b) of the flow channel 10 in an LE-type sensor should be at least two, and preferably three to four, times larger than the largest particle expected to occur in the sample of interest. Otherwise, frequent clogging of the flow cell is inevitable, thus negating one of the principal advantages of the SPOS technique over an alternative single-particle sensing technique known as xe2x80x9celectro-zone,xe2x80x9d or xe2x80x9cresistive-pore,xe2x80x9d sensing (e.g. the xe2x80x9cCoulter counter,xe2x80x9d manufactured by Beckman-Coulter Inc, Hialeah, Fla.).
One of the previously established ways of increasing the sensitivity of a conventional SPOS-type sensor is to use the method of light scattering (LS), rather than light extinction. With the LS technique the background, or baseline, signal is ideally zero in the absence of a particle in the OSZ. (In reality, there is always some low-level noise due to scattering from contaminants and solvent molecules, plus contributions from the light source, detector and amplifier.) Therefore, the height of the detected signal pulse due to a particle passing through the OSZ can be increased, for a given particle size and composition, simply by increasing the intensity of the light source. This simple expedient has resulted in sensors that can detect individual particles as small as 0.2 xcexcm or smaller.
Fortunately, by adopting a completely different measurement approach, significantly higher sensitivity and coincidence concentration can be achieved from an SPOS device than is provided by a conventional LE or LS sensor. The resulting new apparatus and method form the basis of the present invention. The most significant difference in the optical design of the new sensor concerns the light beam that is used to define the OSZ. Rather than resembling a thin xe2x80x9cribbonxe2x80x9d of light that extends across the entire flow channel (i.e. in the x-y plane, FIG. 1), it now consists of a thin xe2x80x9cpencilxe2x80x9d of light (aligned with the y-axis) that probes a narrow region of the flow channel 10. This beam, typically having an approximately gaussian intensity profile and circular cross section, effectively illuminates only a small fraction of the particles that flow through the sensor. The resulting area of illumination, A0, is much smaller than the value typically found in a conventional sensor, which requires that the beam span the entire width (x-axis) of the flow channel 10. By definition, the intensity of the new beam is highly non-uniform in both the lateral (x-axis) direction and the direction of particle flow (z-axis).
Consequently, particles that pass through the sensor are necessarily exposed to different levels of maximum light intensity (i.e. at z=0), depending on their trajectories. The resulting signal pulse height generated by a particle now depends not only on its size, but also its path through the flow channel 10. Particles that pass through the center of the illuminating beam, where the intensity is highest, will generate LE (or LS) pulses of maximum height for a given size, while those that pass through regions of lesser intensity will produce pulses of corresponding reduced height. Hence, the use of a beam of non-uniform (usually, but not necessarily gaussian) intensity profile gives rise to the so-called xe2x80x9ctrajectory ambiguityxe2x80x9d problem. A number of researchers have attempted to address this problem, using a variety of approaches.
The problem of trajectory ambiguity in the case of remote in-situ measurement of scattered light signals produced by unconfined particles was discussed more than twenty years ago by D. J. Holve and S. A. Self, in Applied Optics, Vol. 18, No. 10, pp. 1632-1652 (1979), and by D. J. Holve, in J. Energy, Vol. 4, No. 4, pp. 176-183 (1980). A mathematical deconvolution scheme, based on a non-negative least-squares (NNLS) procedure, was used to xe2x80x9cinvertxe2x80x9d the set of measured light scattering pulse heights produced by combustion particles moving in free space. The measurement volume was defined by a ribbon (elliptical) beam with a gaussian intensity profile and an off-axis distant pinhole and detector, reverse imaged onto the beam. Holve et al explicitly rejected the well-known method of matrix inversion, as it was said to be ineffective when applied to their typical light scattering data. From the results and explanation provided, it is apparent that the resolution and accuracy of the PSDs that could be obtained using their light scattering scheme and NNLS deconvolution procedure were relatively poor. Multimodal distributions required relatively widely spaced particle size populations in order to be resolved reasonably xe2x80x9ccleanlyxe2x80x9d using the referenced apparatus and method.
As disclosed in the Holve articles, the measurement region from which the scattered light signal is detected originates from a portion of the cross section of the illuminating beam. As will be discussed, the present invention also utilizes a beam that is spatially non-uniform in intensity, preferable having a circular gaussian profile. However, the present invention fully xe2x80x9cembracesxe2x80x9d this non-uniformity. That is, the measurement zone encompasses the entire cross section of the beam and not just the central region of highest (and least-variable) intensity. The particles to be counted and sized are caused to flow uniformly through a confined, well-defined space (flow channel) where the fraction of particles of any given size that is measured is fixed and ultimately known. The region from which data are collected is similarly fixed and well-defined and relatively immune to vibrations and optical misalignment. Given the inherent stability and different nature of the physical design associated with the present invention, it should not be surprising that the PSD results possess not only high sensitivity but also superior, unprecedented particle size resolution compared to the results obtained from the Holve approach. It is observed also that Holve""s system is necessarily confined to light scattering as the means of detection. By contrast, the novel apparatus and methods taught in the present invention make possible sensors that are equally effective based on light scattering or light extinction.
Partly because of the limited quality of the PSD results that could be achieved using the apparatus and method described by Holve et al, there was subsequent recognition of the need to develop alternative methods that would permit gaussian beams to be used effectively for particle size determination. Of course, the simplest remedy, if appropriate, was seen to be elimination of the gaussian beam, itself, that is the source of the problem. Foxvag, in U.S. Pat. No. 3,851,169 (1974), proposed altering the intensity distribution of the laser beam, in order to reduce the non-uniformity inherent in its gaussian profile. Separately, G. Grehan and G. Gouesbet, in Appl. Optics, Vol 25, No. 19, pp 3527-3537 (1986), described the use of an xe2x80x9canti-gaussianxe2x80x9d correcting filter in an expanded beam before focusing, thereby producing a xe2x80x9ctop-hatxe2x80x9d beam profile, having substantially uniform intensity over an extended region. Fujimori et al, in U.S. Pat. No. 5,316,983 (1994), used a xe2x80x9csoftxe2x80x9d filter to convert a gaussian laser beam into a flattened intensity distribution.
Other proposals involved physically confining the flowing particles, so that they are forced to pass through the central portion of the laser beam, where the intensity is substantially uniform. An example is described by J. Heyder, in J. Aerosol Science, Vol 2, p. 341 (1971). This approach was also adopted by Bowen, et al, in U.S. Pat. No. 4,850,707 (1989), using a focused elliptical laser beam with a gaussian intensity profile, with a major axis much longer than the width of a hydrodynamically-focused xe2x80x9cchannelxe2x80x9d containing the flowing particles. All of the particles are therefore exposed to substantially the same maximum intensity as they flow through the beam.
An early proposal for accommodating gaussian beams, proposed by Hodkinson, in Appl. Optics, Vol. 5, p. 839 (1966), and by Gravitt, in U.S. Pat. No. 3,835,315 (1974), was to determine the ratio of the peak scattered intensity signals detected simultaneously at two different scattering angles. This ratio is ideally independent of the intensity incident on the particle and, according to Mie theory, is uniquely related to its size. The reliability of this method was improved using the proposal of Hirleman, Jr., et al, in U.S. Pat. No. 4,188,121 (1980). The peak scattered intensities at more than two scattering angles are measured and the ratios of all pairs of values calculated. These ratios are compared with calibration curves in order to establish the particle diameter.
Several methods were suggested for selecting only those particles that have passed substantially through the center of the gaussian beam. A scheme for collecting off-axis scattered light from a distant, in-situ measurement volume, similar to the apparatus used by Holve et al, was described by J. R. Fincke, et al, in J. Phys. E: Sci. Instrum., Vol 21, pp. 367-370 (1988). A beam splitter is used to distribute the scattered light between two detectors, each having its own pinhole aperture. One of the apertures is smaller than the beam waist in the measurement volume. Its detector is used to xe2x80x9cselectxe2x80x9d particles suitable for measurement by the second detector, having a considerably larger aperture, ensuring that they pass substantially through the center of the beam, and therefore are eligible for counting and sizing. Notwithstanding the simplicity and apparent attractiveness of this approach, it was ultimately rejected by the authors, because of the difficulty of maintaining precise, stable alignment of the various optical elements. (This rejection is not unrelated to the limited quality of the PSD results obtained by Holve et al, alluded to above.)
Another set of proposed methods suggested the use of two concentric laser beams of different diameters, focused to a common region, through which particles are allowed to transversely flow, with the outside beam significantly larger in diameter than the inner beam. Two detectors are used to measure the amplitudes of light signals scattered by particles passing through each respective beam, distinguished by different wavelength (color) or polarization. Only those particles that pass through the central portion of the larger measurement beam, where the intensity is substantially uniform, produce signals from the smaller xe2x80x9cvalidatingxe2x80x9d beam. Schemes using beams of two different colors are described by Goulas, et al, in U.S. Pat. No. 4,348,111 (1982), and Adrian, in U.S. Pat. No. 4,387,993 (1983). A variation on the concentric two-beam method is described by Bachalo, in U.S. Pat. No. 4,854,705 (1989). A mathematical formulation is used to process the two independently measured signal amplitudes together with the known beam diameters and intensities to determine the particle trajectory and, ultimately, the particle size. A variation on this approach is described by Knollenberg, in U.S. Pat. No. 4,636,075 (1987), using two focused, concentric beams distinguished by polarization. An elongated, elliptical beam shape is used to reduce the ratio of beam diameters needed to achieve acceptable particle size resolution and higher concentration limits.
Yet another variation of the two-beam approach is described by Flinsenberg, et al, in U.S. Pat. No. 4,444,500 (1984). A broad xe2x80x9cmeasuringxe2x80x9d beam and a narrower xe2x80x9cvalidatingxe2x80x9d beam are again utilized, but in this case the latter is located outside the former, allowing both beams to have the same color and polarization. The plane containing the axes of the two beams is aligned parallel to the flow velocity of the particles. Achieving coincidence of two scattering signals detected separately from each beam ensures that the only particles to be counted and sized are those that have traversed the narrow beam, and hence the central region of the broad, measuring beam. Still another variation of the two-beam approach is described by Hirleman, Jr., in U.S. Pat. No. 4,251,733 (1981). Through the use of two physically separated gaussian beams, the particle trajectory can be determined from the relative magnitudes of the two scattered light signal pulses. This, in turn, permits the intensity incident on the particle everywhere along its trajectory to be calculated, from which the particle size can be determined.
Other proposals take advantage of an interferometric technique commonly utilized in laser Doppler velocimetryxe2x80x94i.e. crossing two coherent laser beams to obtain a fixed fringe pattern in a spatially localized region. The particle size can be determined from the peak scattering intensity, provided differences in trajectory can be accounted or compensated for. A straightforward scheme was proposed by Erdmann, et al, in U.S. Pat. No. 4,179,218 (1979), recognizing that a series of scattered light pulses is produced by each particle, related to the number of fringes through which it passes. The number of pulses establishes how close the particle has approached the center of the xe2x80x9cprobexe2x80x9d volume established by the fringe pattern, where the number of fringes is greatest and the intensity is brightest, corresponding to the center of each gaussian beam. An alternative method was proposed by C. F. Hess, in Appl. Optics, Vol. 23, No. 23, pp. 4375-4382 (1984), and in U.S. Pat. No. 4,537,507 (1985). In one embodiment, two coherent beams of unequal size are crossed, forming a fringe pattern. The small beam xe2x80x9cidentifiesxe2x80x9d the central region of the larger beam, having substantially uniform (maximal) intensity. A signal that contains the maximum a.c. modulation indicates that the particle has passed through the center of the fringe pattern and, hence, the middle of the large beam. The particle size is extracted from the xe2x80x9cpedestalxe2x80x9d (d.c.) signal after low-pass filtering removes the a.c. component. In a second embodiment, two crossed laser beams of one color are used to establish a fringe pattern at the center of a third, larger beam of a second color. A first detector establishes from the magnitude of the a.c. component of the scattered light signal whether a particle has passed substantially through the center of the fringe pattern. If so, the pulse height of the scattered light produced by the large beam, obtained from a second detector, is recorded. Bachalo, in U.S. Pat. No. 4,329,054 (1982), proposed distinguishing the central portion of a fringe pattern, corresponding to the central region of each gaussian beam, by using an additional small xe2x80x9cpointerxe2x80x9d beam of different color or polarization, responding to a separate detector means.
Finally, assorted other techniques have been proposed for addressing the gaussian beam/trajectory ambiguity problem. Bonin, et al, in U.S. Pat. No. 5,943,130 (1999), described a method for rapidly scanning a focused laser beam through a measurement volume, resulting in a scattered intensity pulse each time the beam crosses a particle. Given the high scanning frequency and velocity and the relatively low particle velocity, each particle is scanned several times while it is in the measurement volume. The resulting series of pulses can be fitted to the beam intensity profile and the maximum of the gaussian fit mapped to a particle diameter using a calibrated response function that correlates particle size with scattered light intensity. DeFreez, et al, in U.S. Pat. No. 6,111,642 (2000), proposed a xe2x80x9cflow aperturingxe2x80x9d technique. A particle/fluid delivery nozzle is designed so that the lateral velocity profile of the emerging particles approximately matches the gaussian intensity profile of the laser beam. The reduction in incident light level due to increasing distance of the particle trajectory from the beam axis is compensated approximately by the increase in integration time of the scattering signal, due to the lower velocity. The net integrated scattering signal is therefore ideally independent of the trajectory. An improvement was proposed by Girvin, et al, in U.S. Pat. No. 6,016,194 (2000), using a linear detector array to individually detect the scattered light signals associated with substantially each particle trajectory. The gain of each detector element can be adjusted to compensate for variations that remain in the net signal response of the system in the lateral direction, due to incomplete matching of the nozzle velocity and laser beam intensity profiles, differences in individual detector efficiencies and other effects.
It is the object of the invention to provide an SPOS device and method which provide significantly higher sensitivity and the ability to respond effectively to fluid suspensions which are relatively concentrated with a higher concentration of particles than is usual in the art and which, therefore, need not be diluted to the same degree as is required with prior art SPOS devices.
An SPOS device according to the invention establishes flow of the suspension through a physically well-defined measurement flow channel. A relatively narrow beam of light is directed through the measurement flow channel to illuminate an optical sensing zone within the measurement flow channel, the beam of light and the optical sensing zone being of such size relative to the size of the measurement flow channel that the SPOS device responds to a small fraction of the total number of particles flowing through the measurement flow channel with the result that the SPOS device will respond effectively to a relatively concentrated fluid suspension. The beam illuminates the optical sensing zone non-uniformly, having a central maximum intensity portion and a continuum of lesser intensities for positions spaced from the maximum intensity portion, so that some of the particles have trajectories through the maximum intensity portion, others of the particles have trajectories through the lesser intensity portions, and still others of the particles may have trajectories outside the zone.
The measurement flow channel has a thickness dimension axially of the beam of light, a width, or lateral, dimension transverse to the beam and a flow direction perpendicular to the thickness and width dimensions. The beam, which is much narrower than the measurement flow channel in the width direction, may be focused with a depth of field which is substantially larger than the thickness dimension, so that the beam has an effective width which does not vary substantially over the thickness dimension. The effective width which is defined as the width between opposing positions in the beam at which said lesser intensities have fallen to a given fraction, such as 1/e2, of said maximum intensity, is chosen so that particles can be effectively sized over the range of particles to be sized and is typically substantially one half the size of the largest particle to be sized. The intensity of the beam is highly non-uniform in the lateral direction and the direction of particle flow and may have a gaussian intensity profile. The beam may be circular in cross-section or elliptical, being wider transverse to the beam in the direction perpendicular to particle flow than in the direction parallel to particle flow.
The SPOS device of the invention uses a photo-detector and may operate on a light-extinction or light-scattering principle. Indeed, some sensor embodiments include both detection techniques. The photo-detector detects light from the zone to provide pulse height signals, each responsive to a particle flowing through said zone, the pulse height signals being functions of the sizes and trajectories of detected particles, particles of a given size providing a maximum pulse height signal when flowing through the maximum intensity portion and lesser pulse height signals when flowing through the lesser intensity positions of the zone. The pulse height signals, collectively, form a pulse height distribution (PHD). A statistically significant number of particles of the given size flow through the lesser intensity positions of the zone.
The use of a non-uniform beam creates the xe2x80x9ctrajectory ambiguityxe2x80x9d problem. For this reason, the device and method include means for mathematically deconvoluting the pulse height distribution to provide a particle size distribution of the particles in the suspension. According to the invention, the deconvolution method is an improvement over deconvolution as taught in the prior art. The invention proposes the use of two deconvolution techniques: one using matrix inversion, and the other using successive subtraction.
Both techniques use a matrix. According to this invention, the process of setting up the matrix is simplified. The matrix has column basis vectors, each corresponding to a particular particle size. It has been proposed in the prior art to empirically base the values of all of the column basis vectors on measurements of particles of uniform, known size. Since the matrix may have a large number of columns (32, 64 and 128 are proposed in this application), according to the present invention only one or a few of the column basis vectors, or alternatively, none of them, need be empirically based on measurements of particles of known size. The remaining column basis vectors are computed by interpolation and/or extrapolation from empirically based column basis vectors. It is also proposed by this invention that some, or all, of the column basis vectors can be computed from a theoretical model. If some of them are so computed, the remaining column basis vectors can be computed by interpolation and/or extrapolation from those computed from existing data.
It is proposed to modify a method of deconvolution by matrix inversion. Each column basis vector has a maximum count pulse height at a location for a row which relates to a pulse height channel corresponding to a particle of known size associated with the column basis vector, the maximum count pulse height values for successive columns being arranged in a diagonal of the matrix. The matrix is modified by setting all terms below the diagonal to zeroxe2x80x94that is to say, all terms corresponding to pulse height values greater than the maximum count pulse height value in a column are set to zero. This improves the accuracy, signal/noise ratio and reproducibility of the result.
The proposed method of deconvolution by successive subtraction involves setting up a matrix having a plurality of columns each containing a basis vector comprising a pulse height distribution of particles of a known size, each successive column containing a basis vector for particles of successively larger sizes, and a maximum-size basis vector containing a pulse height distribution for maximum size particles. The successive subtraction algorithm comprises the steps of
starting with the basis vector with its maximum count value in the row corresponding to the largest pulse height;
scaling a column basis vector by a factor corresponding to the value of the row in the PHD that matches the column number; subtracting said scaled basis vector from the PHD to form an element of the deconvoluted PHD (dPHD), leaving an intermediate PHD vector with a smaller total number of particles;
and repeating this process using the remaining basis vectors until the entire PHD has been substantially consumed and all the elements of deconvoluted dPHD have been formed.
Using a calibration curve of the relationship of pulse height and diameter, each deconvoluted pulse height value in the dPHD is translated into a unique particle diameter associated with this pulse height value yielding a raw particle size distribution, PSD. The raw PSD is converted into a final PSD by normalizing the raw PSD by multiplying it by the value 1/xcfx86d, where xcfx86d is the fraction of particles actually detected by said device for particles of each size, d.
When the fluid suspension is relatively concentrated, light extinction type sensors may be affected by turbidity. Compensation for turbidity may be provided in one of three ways. First the baseline voltage levels for turbid and non-turbid liquids are sensed, a ratio is computed, and this ratio is used to increase the amplitude of the light-extinction signal such that the baseline voltage level for the turbid liquid is increased to approximately the baseline voltage level for the non-turbid liquid. Second, the pulse height signals generated by the turbid liquid are corrected by the computed ratio. Third, the intensity of the starting beam of light is adjusted in response to the ratio to compensate for turbidity.
An embodiment of the invention includes both a light-extinction (LE) detector and a light-scattering (LS) detector. Scattered light from the zone is passed to the (LS) detector through a mask to select light scattered between a first and a second angle to the beam. Light transmitted through the zone is directed to the LE detector. Another embodiment uses an optical fiber for conveying light from a light source to the optical sensing zone and projecting said light through the zone and an optical fiber for conveying the light from the zone to a LE detector. Scattered light from the zone is passed through a mask to select light scattered between a first and a second angle to the beam and this scattered light is collected by the LS detector. A further embodiment comprises a light source, a beam splitter for providing two light beams directed through a pair of optical sensing zones positioned within the measuring flow channel, each beam having an effective width compatible with a different range of particle sizes. Another embodiment comprises a light-scattering detector and means for passing a portion of the light through one of a plurality of masks located on a rotatable wheel, and means for selecting one of these masks by rotating the wheel to a desired orientation, each mask defining different angles between which the light is scattered and collected. A final embodiment projects a relatively wide collimated beam through the optical sensing zone. The beam has a central axis, and an acceptance aperture captures only those light rays that closely surround the central axis of the beam. This reduces the effective width of the beam to a width in a direction transverse to the axis of the light beam that is substantially one-half the size of the largest particle to be sized. An optical fiber couples the light rays to a detector.